hunger vs ache

hunger and ache both are nouns.

Word	Noun	Adjective	Verb	Adverb
hunger	Yes	No	Yes	No
ache	Yes	No	Yes	No

As verbs, ache is a hypernym of hunger; that is, ache is a word with a broader meaning than hunger:

Other hypernyms of hunger include hurt, smart.

hunger (noun)	ache (noun)
strong desire for something (not food or drink)	a dull persistent (usually moderately intense) pain
a physiological need for food; the consequence of food deprivation

hunger (verb)	ache (verb)
be hungry; go without food	have a desire for something or someone who is not present
have a craving, appetite, or great desire for	be the source of pain
feel the need to eat	feel physical pain